Topics in Description Logics of Typicality and Quantification Neglect

Description Logics (DLs) are a family of formalisms conceived to represent knowledge in a well-defined, decidable and computationally tractable way. DLs are fragments of first-order logic and inherit some of its properties, such as monotonicity. As their goal is to represent knowledge, handling concepts in a human-inspired fashion can be useful. Typicality is a well-studied phenomenon of human conceptualisation. It manifests itself in grades of representativeness relative to concept membership, enabling non-monotonic reasoning. Researchers have been exploring the intersection between DLs and typicality from different perspectives, creating a rich and still not fully explored landscape. Our first goal is to identify the main tendencies and the most pressing problems of the area. This is already complete and resulted in a yet to be published survey paper. The second part aims to explore further a serious issue affecting DLs of typicality: quantification neglect, i.e., the inability of most typicality DLs to apply defeasible information to concepts nested within quantifiers. We intend to extend the recent typicality models' approach presented in Pensel (2018) to more expressive DLs that nonetheless have the canonical model property, such as Horn-DLs. Further stages may include comparisons with other systems that may handle quantification neglect differently.

Mentor: Laura Giordano

Pointwise Circumscription in Description Logics: A Local Approach to Non-Monotonicity

In this work, we aim to combine Description Logics (DLs) with pointwise circumscription. Providing a picture of the well-established circumscribed DLs, we underline the so far pursued research towards a local form of minimization that is computationally less costly and we describe our preliminary steps towards the complexity classification of reasoning in DLs with pointwise circumscription.

Mentor: Piero Bonatti

Detecting and Resolving Counterintuitive Consequences in Law as Legal Debugging

Recently, there have been many approaches for revising logic programs that represent the interpretation of the statutes in order to resolve legal conflicts. Unfortunately, unlike revisions to resolve legal conflicts, revisions to meet social expectations cannot be done automatically. Furthermore, as early works in AI and Law have suggested, formalizing legal changes for meeting social expectations requires debugging-like mechanisms in legal reasoning systems. However, there are no theoretical foundations of debugging in law to our knowledge. Therefore, in this proposal, we propose Legal Debugging, extending from Algorithmic Debugging in software engineering, for judges in civil law systems to detect and resolve counterintuitive consequences in law. Legal Debugging consists of two main algorithms, namely Culprit Detection Algorithm and Culprit Resolution Algorithm. Culprit Detection Algorithm assists the user to discover more counterintuitive consequences by checking with the user whether related consequences are counterintuitive until the user finds no more counterintuitive consequences related. The last found counterintuitive consequence, called a culprit, is determined as a root cause of such counterintuitive consequences. Culprit Resolution Algorithm assists the user to revise the rule-base representing statutes by letting the user choose necessary conditions that indicate the exceptional situations in the case.

Mentor: Francesca Toni

Active Learning of Queries under Ontologies

Query Learning can support various tasks when working with unfamiliar knowledge bases, e.g. query construction or data mining. However, it is not yet known which classes of queries are efficiently learnable under description logic ontologies. Of particular interest is efficient learnability of queries in Angluin's model of active learning, where the learning algorithm may ask a teacher questions to get more information. In order to enable query learning in practical applications, combinations of query language and ontology language should be identified that allow efficient query learning in this model. First results have been obtained that give efficient learning algorithms for certain classes of queries under ontologies formulated in DL-Lite or EL respectively. However, the important question whether all conjunctive queries are efficiently learnable under description logic ontologies remains open.

Mentor: Ana Ozaki

Knowledge Representation Formalisms for Hybrid Intelligence

Knowledge graphs (KGs) have a significant role in storing and providing access to global knowledge, common and accessible to both human and artificial agents, representing knowledge for different agents in Hybrid Intelligence (HI) settings. Unfortunately, providing suitable formalisms to work with complex, conflicting, dynamic and contextualised knowledge is still a big challenge. Therefore, we investigate the usage of knowledge representation formalisms that allows hybrid intelligence systems to adapt and work with complex, conflicting, dynamic and contextualized knowledge.

Mentor: Emanuel Sallinger

Formal Foundations of Incremental Dynamic Answer Set Programming

Extensions of Answer Set Programming (ASP) with language constructs from dynamic and temporal logics provide an expressive computational framework for modeling dynamic applications. In my PhD studies, I explore the logical foundations of temporal and dynamic ASP. I focus on the identification and study of fragments of temporal and dynamic logics, as well as the optimization of translations involving those logics.

Mentor: Martin Gebser

Reasoning with Ontologies for Non-Player Character Decisions in Games

Artificial intelligence (AI) techniques for Non-Player Character (NPC) decision-making based on logical reasoning with ontologies are almost absent from the academic and industrial game literature. We propose to take advantage of the high expressiveness of rule-based systems and their planning potential with backward chaining on an inference engine to develop more sophisticated action plans. We believe that logic programming, successfully used in other fields, with the addition of the Well-Founded Semantics (WFS) as well as the Belief-Desire-Intention framework, could improve the sometimes insufficient credibility of the NPCs and their reasoning capabilities.

Mentor: Laurent Perrussel

Aggregate Queries in Ontology-Based Data Access

In ontology-mediated query answering (OMQA), data is enriched with an ontology, which serves both to provide a user-friendly vocabulary for query formulation and to capture domain knowledge that is exploited at query time to obtain a more complete set of answers. Most works on OMQA assume that user queries are expressed as conjunctive queries, while many other types of queries might be useful in practice. This thesis summary presents our ongoing PhD project on aggregate queries in ontology-based data access.

We recall existing approaches to integrate aggregate functions in OMQA, in particular counting features, and our contribution in this direction. We also summarize analysis of the computational complexity of answering such counting queries, including the identification of tractable cases and a fine-grained analysis we conducted at the level of the ontology-mediated query. Finally, we present a recent contribution exploring this problem outside of the DL-Lite family, and highlight the various possible directions for future work from implementation considerations to theoretical integration of other kinds of aggregate functions.

Mentor: Carsten Lutz

Ranking Extensions in Abstract Argumentation

Extension-based semantics in abstract argumentation provide a criterion to determine whether a set of arguments is acceptable or not. In this paper, we present the notion of extension-ranking semantics, which determines a preordering over sets of arguments, where one set is deemed more plausible than another if it is somehow more acceptable. We obtain extension-based semantics as a special case of this new approach, but it also allows us to make more fine-grained distinctions, such as one set being “more complete” or “more admissible” than another.

Mentor: Stefan Woltran